Hyperbolic cross approximation / Dinh Dũng, Vladimir Temlyakov, Tino Ullrich ; editor for this volume: Sergey Tikhonov.
Dũng, Dinh, author.; Temlyakov, Vladimir, 1953- author.; Ullrich, Tino, 1980- author.; Tikhonov, Sergey, 1976- editor.
2018
QA221
Available Online

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Title Hyperbolic cross approximation / Dinh Dũng, Vladimir Temlyakov, Tino Ullrich ; editor for this volume: Sergey Tikhonov.
Author Dũng, Dinh, author.
ISBN 9783319922409 (electronic book)
3319922408 (electronic book)
9783319922393
3319922394
DOI https://doi.org/10.1007/978-3-319-92240-9
Published Cham, Switzerland : Birkhäuser, 2018.
Language English
Description 1 online resource (xi, 218 pages) : illustrations
Other Standard Identifiers 10.1007/978-3-319-92240-9 doi
Call Number QA221
Dewey Decimal Classification 511/.4
Summary This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying multivariate approximation. Multivariate problems have proven to be considerably more difficult than their univariate counterparts, and recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents essential findings on and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many of the important open problems explored here will provide both students and professionals with inspirations for further research.-- Provided by publisher.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed November 12, 2018).
Added Author Temlyakov, Vladimir, 1953- author.
Ullrich, Tino, 1980- author.
Tikhonov, Sergey, 1976- editor.
Series Advanced courses in mathematics, CRM Barcelona, 2297-0304
Available in Other Form Print version: 9783319922393
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Introduction
Trigonometric polynomials
Function spaces on T^d
Linear approximation
Sampling recovery
Entropy numbers
Best m-term approximation
Numerical integration
Related problems
High-dimensional approximation
Appendix.

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